Abstract
In this paper I consider choice correspondences defined on a novel domain: the decisions are assumed to be taken not by individuals, but by committees, whose membership is observable and variable. In particular, for the case of two alternatives I provide a full characterization of committee choice structures that may be rationalized with two common decision rules: unanimity with a default and weighted majority.
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Notes
These results apply when nothing is known about the group composition. When the size of the committee is known, there exist restrictions implied by various group choice rules on the minimal choice cycle length, which have been studied since Nakamura (1979).
Thus, in a legislature no formal vote may be taken on an issue since the parliamentary leaders know that it would fail anyway.
See, for instance, Vargas (1996) for a discussion of the role—and lack of precedential authority—of the writ of amparo in Mexican legal system.
The details of the case assignment are described in Articles 49 and 50 of the Reglamento Interno (Internal Rules) of the Colombian Constitutional Court (1992). The author thanks Juan Bertomeu for drawing his attention to this arrangement.
The reason I am only considering choice functions, rather than choice correspondences in this section—an assumption that will be relaxed later—is that the unanimity rule, as here defined, always produces a unique choice.
That is, if \(S,T\in \mathcal {E}\), then \(S\cup T\in \mathcal {E}\).
This of course, covers the case when \(\mathcal {E}\) has a single element.
It follows from the proof of the proposition above that, except in the trivial case where the choice is the same for all committees, the choice of the default is uniquely implied by the data.
See, for instance, Feddersen and Pesendorfer (1996).
For a recent survey of such studies see, for instance, Kugler et al. (2012). The committee overlap typically arises there from rematching committee members in order to avoid repeated interaction effects between experimental subjects.
Indeed, if we consider Example 2 above, we obtain the following system of \( K=7\) inequalities:
$$\begin{aligned} \left\{ \begin{array}{c} w_{1}+w_{2}+w_{3}>0 \\ w_{1}>0 \\ w_{2}>0 \\ w_{3}>0 \\ -w_{1}-w_{2}>0 \\ -w_{1}-w_{3}>0 \\ -w_{2}-w_{3}>0 \end{array} \right. \end{aligned}$$which, obviously, has no solution. The dual problem solves with \( r_{1}=r_{2}=r_{3}=r_{4}=3\) and \(r_{5}=r_{6}=r_{7}=2\).
On the other hand, if the choice of the committee \(\left\{ 2,3\right\} \) were not observed the corresponding system would have been (\(K=5\)):
$$\begin{aligned} \left\{ \begin{array}{c} w_{1}+w_{2}+w_{3}>0 \\ w_{2}>0 \\ w_{3}>0 \\ -w_{1}-w_{2}>0 \\ -w_{1}-w_{3}>0 \end{array} \right. \end{aligned}$$which would be solved, for instance, by the weight vector \(w=\left( -3,2,2\right) \).
Note that the example above shows that a stronger indirect extension could be imposed here. However, reinforcement is more intuitive, so I stick to it as a necessary implication of rationalizability.
The naming suggestion for this axiom, originally introduced in Gomberg (2011), belongs to Norman Schofield.
As noted above, in the binary choice settings of Sects. 2 and 3, if individuals are merely aggregating preferences they would have no incentives for strategic voting. If, however, they share an underlying preference but aggregate information, strategic voting incentives would emerge, as in Feddersen and Pesendorfer (1996).
References
Apesteguia J, Ballester M, Masatlioglu Y (2014) A foundation for strategic agenda voting. Games Econ Behav 87:91–99
Corte Constitucional de Colombia (1992) Reglamento Interno, retrieved at http://www.corteconstitucional.gov.co/lacorte/reglamento.php
Deb R (1976) On constructing generalized voting paradoxes. Rev Econ Stud 43:347–351
Degan A, Merlo A (2009) Do voters vote ideologically. J Econ Theory 144:1868–1894
Feddersen T, Pesendorfer W (1996) The swing voter’s curse. Am Econ Rev 86:408–424
Fishburn P (1970) Utility theory for decision-making. Wiley, New York
Fisburn P (1986) Axioms of subjective probability. Stat Sci 1:335–345
Gersbach H, Hahn V (2008) Should the individual voting records of central bankers be published? Soc Choice Welf 30:655–683
Gomberg A (2011) Vote revelation: empirical content of scoring rules. In: Schofield N, Caballero G (eds) Polit Econ Democr Voting. Springer, Berlin, Heidelberg, pp 411–417 2011
Houthakker H (1950) Revealed preference and the utility function. Economica 17:159–174
Kalandrakis T (2010) Rationalizable voting. Theor Econ 5:93–125
Kraft C, Pratt J, Seidenberg A (1959) Intuitive probability on finite sets. Ann Stat 30:408–419
Kugler T, Kausel E, Kocher M (2012) Are groups more rational than individuals? A review of interactive decision making in groups. Wiley Interdiscip Rev Cognit Sci 3:471–482
McGarvey D (1953) A theorem on the construction of voting paradoxes. Econometrica 21:608–610
May Kenneth O (1952) A set of independent necessary and sufficient conditions for simple majority decision. Econometrica 20:680–684
Myerson R (1995) Axiomatic derivation of the scoring rules without the ordering assumption. Soc Choice Welf 12:59–74
Nakamura K (1979) The vetoers in a simple game with ordinal preferences. Int J Game Theory 5:55–61
Sibert A (2003) Monetary policy committees: individual and collective reputations. Rev Econ Stud 70:649–665
Smith J (1973) Aggregation of preferences with variable electorate. Econometrica 41:1027–1041
Vargas J (1996) Rebirth of the supreme court of Mexico: an appraisal of president Zedillo’s judicial reform of 1995. Am Univ J Int Law Policy 11:295–341
Young P (1975) Social choice scoring functions. SIAM J Appl Math 28:824–838
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An earlier verison of this paper was previously circulated under the title Vote revelation: empirical consequences of scoring. I would like to thank Attila Ambrus, David Austen-Smith, Juan Bertomeu, Rajat Deb, Diego Dominguez, Federico Echenique, Konrad Grabiszewski, Paola Manzini, Marco Mariotti, César Martinelli, Yusufcan Masatlioglu, Nicolas Melissas, Martin Osborne, Michael Richter, Ariel Rubinstein, Tridib Sharma, Levent Ulku, Radovan Vadovic and the participants of the ICOPEAI 2010 conference at Vigo (which gave rise to the volume in which my earlier note-Gomberg 2011-on a related topic was published), 2011 APET conference in Bloomington, IN, 2011 SAET conference in Faro, Portugal, the 2012 World Congress of the Game Theory Society, the NES 20th Anniversary Decision Theory Workshop in Moscow and the Winter 2013 Computational Social Choice Workshop in Singapore, 2013 ITAM Decision Theory Workshop, 2013 NYU Alumni Conference and the 2014 Social Choice and Welfare Meetings, as well as the seminar participants at CEFIR, ITAM and the SMU for valuable ideas. My particular gratitude goes to Andrew Caplin, conversations with whom helped me formulate this problem. Financial support of Associación Mexicana de Cultura, A.C. is gratefully acknowledged.
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Gomberg, A. Revealed votes. Soc Choice Welf 51, 281–296 (2018). https://doi.org/10.1007/s00355-018-1116-6
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DOI: https://doi.org/10.1007/s00355-018-1116-6